Problem: I have 10 distinguishable socks in my drawer: 4 white, 4 brown, and 2 blue.  In how many ways can I choose a pair of socks, provided that I get two socks of the same color?
Solution: The socks must be either both white, both brown, or both blue.  If the socks are white, there are $\binom{4}{2} = 6$ choices.  If the socks are brown, there are $\binom{4}{2} = 6$ choices.  If the socks are blue, there is $\binom{2}{2} = 1$ choice.  So the total number of choices for socks is $6 + 6 + 1 = \boxed{13}$.